Quantities and Units in A-Level Physics | A-Level 物理量纲与单位

📚 Quantities and Units in A-Level Physics | A-Level 物理量纲与单位

In Edexcel A-Level Physics, Topic 3 Quantities and Units is the foundation for every calculation, practical skill and written explanation you will meet. It covers SI base units, derived units, prefixes, unit conversion, equation homogeneity, dimensional analysis, vectors and scalars, and the correct use of significant figures and uncertainties.

在 Edexcel A-Level 物理中，第3单元“量纲与单位”是后续所有计算、实验技能和文字解释的基础。它涵盖国际单位制基本单位、导出单位、词头、单位换算、方程量纲一致性、量纲分析、矢量与标量，以及有效数字和不确定度的正确使用。

1. SI Base Quantities and Units | 国际单位制基本量与单位

All physical quantities are expressed in terms of seven SI base quantities. Each base quantity has a defined base unit and symbol. You must know these exactly for Edexcel examinations because derived units are built from them.

所有物理量都可以用七个国际单位制基本量表示。每个基本量都有规定的单位名称和符号。你必须准确掌握这些内容，因为导出单位都是由基本单位组合而来的。

Base quantity	Base unit	Symbol
length	metre	m
mass	kilogram	kg
time	second	s
electric current	ampere	A
temperature	kelvin	K
amount of substance	mole	mol
luminous intensity	candela	cd

Length, mass and time are the most frequently used base quantities in mechanics. Electric current is the extra base quantity needed for electricity topics, while kelvin, mole and candela appear in thermal physics, gas laws and light measurements.

长度、质量和时间是力学中最常用的基本量。电流是电学部分所需的额外基本量，而开尔文、摩尔和坎德拉则出现在热物理、气体定律和光测量中。

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2. Derived Quantities and Special Unit Names | 导出量与专用单位名称

Derived quantities are formed by multiplying or dividing base quantities. Some derived units have special names, such as the newton for force and the joule for energy. It is important to express these special units in base units when checking equations.

导出量由基本量相乘或相除得到。一些导出单位有专用名称，例如力的单位牛和能量的单位焦。检查方程时，把这些专用单位写成基本单位非常重要。

Derived quantity	Relation	Derived unit	In base units
speed	distance ÷ time	m s⁻¹	m s⁻¹
acceleration	velocity ÷ time	m s⁻²	m s⁻²
force	mass × acceleration	N	kg m s⁻²
energy or work	force × distance	J	kg m² s⁻²
power	energy ÷ time	W	kg m² s⁻³
pressure	force ÷ area	Pa	kg m⁻¹ s⁻²
electric charge	current × time	C	A s
potential difference	energy ÷ charge	V	kg m² s⁻³ A⁻¹
resistance	potential difference ÷ current	Ω	kg m² s⁻³ A⁻²

o see how force depends on mass, length and time. This is central to homogeneity checks and dimensional analysis.

例如，牛并不是基本单位。写出 1 N = 1 kg m s⁻² 可以让你看清力与质量、长度和时间的关系。这对量纲一致性检查和量纲分析至关重要。

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3. Prefixes and Scientific Notation | 词头与科学计数法

Very large and very small quantities are written using prefixes or scientific notation. You must be able to convert between prefix form, decimal form and standard form without a calculator in many cases.

非常大和非常小的物理量用词头或科学计数法表示。你必须能够在很多情况下不借助计算器完成词头形式、小数形式和标准形式之间的转换。

Prefix	Symbol	Factor
peta	P	10¹⁵
tera	T	10¹²
giga	G	10⁹
mega	M	10⁶
kilo	k	10³
centi	c	10⁻²
milli	m	10⁻³
micro	μ	10⁻⁶
nano	n	10⁻⁹
pico	p	10⁻¹²
femto	f	10⁻¹⁵

⁻⁶ s into microseconds. Always write the prefix as a power of ten first, then adjust the decimal point carefully.

常见的考试任务是把 25 mA 转换成安，或把 3.2 × 10⁻⁶ s 转换成微秒。先写出词头对应的十的幂，再小心移动小数点。

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4. Converting Units and Non-SI Units | 单位换算与非国际单位制单位

Some quantities are given in non-SI units that are still used in daily life or specific fields. You must convert them into SI units before substituting into most A-Level formulas.

一些物理量使用日常生活中或特定领域仍在使用的非国际单位制单位。在代入大多数 A-Level 公式之前，必须先把它们换算成国际单位制单位。

1 km h⁻¹ = 1000 m ÷ 3600 s = 0.278 m s⁻¹

For speed, the conversion factor between km h⁻¹ and m s⁻¹ is 1 ÷ 3.6. To convert from m s⁻¹ to km h⁻¹, multiply by 3.6.

对于速度，km h⁻¹ 与 m s⁻¹ 之间的换算系数是 1 ÷ 3.6。从 m s⁻¹ 换算到 km h⁻¹ 时乘 3.6。

1 g cm⁻³ = 0.001 kg ÷ (0.01 m)³ = 1000 kg m⁻³

Density in g cm⁻³ must be multiplied by 1000 to become kg m⁻³. This conversion is especially important in materials and fluids questions.

以 g cm⁻³ 为单位的密度必须乘以 1000 才能变成 kg m⁻³。这种换算在材料和流体问题中尤为重要。

tres, where 1 L = 1 × 10⁻³ m³, and degrees Celsius to kelvin, where T(K) = θ(°C) + 273.15.

其他常见换算包括升到立方米，1 L = 1 × 10⁻³ m³，以及摄氏度到开尔文，T(K) = θ(°C) + 273.15。

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5. Homogeneity of Physical Equations | 物理方程的量纲一致性

An equation is homogeneous if every term on both sides has the same base units. Checking homogeneity is a fast way to identify impossible formulas and to decide whether a given equation could be correct.

如果方程两边每一项都具有相同的基本单位，则该方程是量纲一致的。检查量纲一致性是识别不可能成立的公式、判断某个方程是否可能正确的快速方法。

Consider the equation of motion:

考虑运动方程：

v² = u² + 2 a s

units m s⁻² × m = m² s⁻². Since all three terms are the same, the equation is homogeneous.

这里 v² 和 u² 的单位都是 (m s⁻¹)² = m² s⁻²。2 a s 这一项的单位是 m s⁻² × m = m² s⁻²。由于三项单位相同，该方程量纲一致。

Homogeneity does not prove an equation is the correct physical law, but it does rule out equations with inconsistent units. Constants may be dimensionless or may have units, so always include constants in the unit check.

量纲一致性不能证明一个方程是正确的物理定律，但可以排除单位不一致的方程。常数可能是无量纲的，也可能具有单位，因此检查单位时始终要包含常数。

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6. Dimensional Analysis as a Checking Tool | 量纲分析作为检查工具

Dimensional analysis means working only with units to find the units of an unknown quantity or to verify a derived formula. It is especially useful when you cannot remember the exact relationship.

量纲分析指只用单位来求未知量的单位或验证导出公式。当你记不清确切关系时，它尤其有用。

Example: determine the SI base units of the gravitational constant G from Newton's law of gravitation.

例题：根据牛顿万有引力定律，求引力常数 G 的国际单位制基本单位。

F = G m₁ m₂ / r²

Rearranging gives G = F r² / (m₁ m₂). The units are:

整理得 G = F r² / (m₁ m₂)。单位是：

G = kg m s⁻² × m² ÷ kg² = m³ kg⁻¹ s⁻²

So G is measured in m³ kg⁻¹ s⁻². This matches the unit expected for a constant that relates force, masses and distance.

所以 G 的单位是 m³ kg⁻¹ s⁻²。这符合一个联系力、质量和距离的常数应有的单位。

the ohm, is equivalent to kg m² s⁻³ A⁻². Start from R = V / I and express V in base units.

在电学中，你可以用量纲分析证明电阻单位欧姆等于 kg m² s⁻³ A⁻²。从 R = V / I 开始，把 V 写成基本单位。

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7. Scalars and Vectors: Direction Matters | 标量与矢量：方向很重要

Quantities are classified as scalars or vectors. A scalar has magnitude only, while a vector has both magnitude and direction. This classification affects how units are combined and how quantities are added.

物理量分为标量和矢量。标量只有大小，矢量既有大小又有方向。这种分类会影响单位的组合方式以及物理量的相加方式。

• Scalars: distance, speed, mass, energy, temperature, time, charge, power.
• Vectors: displacement, velocity, acceleration, force, momentum, electric field strength.

标量：路程、速率、质量、能量、温度、时间、电荷、功率。

矢量：位移、速度、加速度、力、动量、电场强度。

The SI units of a vector do not show direction. For example, velocity and speed are both measured in m s⁻¹, but velocity must include a direction statement such as north or 30° above the horizontal.

矢量的国际单位制单位不显示方向。例如，速度和速率都以 m s⁻¹ 为单位，但速度必须包含方向说明，如向北或与水平面成 30°。

When adding vectors, you must use vector addition rather than simple arithmetic. When adding scalars, ordinary addition applies, provided the units match.

矢量相加时必须使用矢量加法，而不是简单的算术加法。标量相加时，只要单位一致，就可以使用普通加法。

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8. Significant Figures and Measurement Uncertainty | 有效数字与测量不确定度

Every measurement has uncertainty, and the number of significant figures you write must reflect the precision of the instrument. Edexcel questions often ask for a final answer to an appropriate number of significant figures.

每次测量都有不确定度，你写出的有效数字位数必须反映仪器的精度。Edexcel 试题经常要求最终答案保留适当的有效数字。

For a single measurement, absolute uncertainty may be half the smallest division on an analogue instrument, or the resolution stated for a digital instrument.

对于单次测量，绝对不确定度可以是模拟仪器最小刻度的一半，或数字仪器标明的分辨率。

percentage uncertainty = (absolute uncertainty ÷ measured value) × 100%

When combining measurements, addition and subtraction combine absolute uncertainties, while multiplication and division combine percentage uncertainties.

组合测量值时，加减运算合并绝对不确定度，乘除运算合并百分不确定度。

rrent is measured as I = 2.00 ± 0.05 A and a resistance as R = 10.0 ± 0.2 Ω, the power P =

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